If Gotham's police cared as much about clearance rates, then the murders committed by the Joker might have been closed just like Gideon's case. A witness saw someone with a criminal record loitering near the scene, and based on that testimony, the police arrested the suspect.
During cross-examination, it was easy to draw contradictory statements from a witness. But under the common law system, such self-contradictory statements were only relatively weak evidence for impeaching a witness's credibility.
For instance, a witness might say they wore yellow on the day of the crime when they had actually worn blue. The root of such inconsistency might lie in flaws in observation and memory. Wrongful convictions did not occur because the witness deliberately committed perjury, but because the witness's unintentional errors created inaccuracies. They had neither motive nor opportunity to lie, and psychology might be needed to expose the issue when necessary.
Human perception differed between dangerous and safe situations. When the Joker encountered those three young men on the train, they were "having fun" with the woman who later became a witness. Then she heard one, two, three, four, five, six gunshots.
Wait. Think carefully—were there six shots, or seven? That was crucial testimony, because an ordinary revolver only held six bullets.
But the key was that no matter who the murderer was, even without surveillance cameras, the bullets left in the bodies could serve as evidence in solving the case.
Only if the killer could not be found would that key evidence never be presented, and no one would know that the murder weapon was a missing police handgun.
After visiting the scene, Gideon's defense lawyer quickly discovered the "flaw." The billiard room was not only very dark, but an advertising sign also blocked Cook's view. Besides, the windowpane was broken.